Study On Some Fixed Points Of Nonlinear Operators And It's Iterative Convergence

The fixed point theorems of nonlinear operators has become an important part of nonlinear analysis, the issue of research has partial differential equations, control theory, economic equilibrium theory and game theory and other fields to obtain a highly successful applications. The most important nonlinear mappings, monotone mappings, accretive and pseudo-contractive mappings, these mappings on the existence of fixed points and iterative convergence of research are particularly important.The paper studies several classes of fixed points of nonlinear operators and iterative convergence. Paper is divided into four parts:In Chapter I, we discusse the nonlinear operator and its fixed point iterative method of the background and status;In Chapter II, we prove, in the metric space some common fixed point theorems for a pair of set-valued mappings and two pair of single-valued mappings, under strict contractive conditions with no compacity and without using continuity;In Chapter III, we prove in the complete metric space, by using pair of self-mapping of the compatibility and weak compatibility condition, the existence and uniqueness of the common fixed points a class of twice power type contraction mapping andφ-type contraction mapping are discussed;In Chapter IV, we prove theφ-pseudocontractive mapping fixed point iteration convergence, introduce a generalized Halpern-Mann type iterative algorithm with errors.In this paper create a new mapping, the introduction of a new iteration, to obtain a new fixed point theorem and a new iteration convergence theorem. And the results presented in this paper generalize and improve the corresponding known ones.